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Quantum and semi-Classical Approaches to J/ ψ SUPPRESSION. Roland Katz. 1 st year PhD student at Subatech (France). Advisor : P.B. Gossiaux. ECT Trento 2013 – 5/04/2013. Summary. Introduction Quantum formalism Quantum results Semi-classical formalism Semi-classical results - PowerPoint PPT Presentation
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ECT Trento 2013 – 5/04/2013
1st year PhD student at Subatech (France)Advisor: P.B. Gossiaux
QUANTUM AND SEMI-CLASSICAL APPROACHES TO J/ψ SUPPRESSION
Roland Katz
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• Introduction• Quantum formalism• Quantum results• Semi-classical formalism• Semi-classical results• Comparison• Conclusion
Summary
Roland Katz – 5/04/2013
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Background? Quarkonia suppression was predicted by Matsui and Satz as a
sign of Quark-Gluon Plasma production in heavy-ion collisions.
Quarkonia suppression has been observed but is still poorly understood.
PhD thesis goal ? Study the evolution of a pair in the QGP by different means.
Explain the observed suppression of the J/ψ suppression as the collision energy increases.
Introduction Quantum Semi-classical Comparison Conclusion
Introduction
Roland Katz – 5/04/2013
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Introduction Quantum Semi-classical Comparison Conclusion
Roland Katz – 5/04/2013
This project goal ?
Study the wavefunction of a pair in an isotropic QGP at thermal equilibrium through:
… then projection onto the J/ψ state.
Results comparison to validate/unvalidate Young and Shuryak* semi-classical approach to J/ψ survival with stochastic Langevin equation.
Quantum approach• Non relativistic Schrödinger equation
Semi-classical approach• Quantum Wigner distribution• Classical, 1st order in ħ, Wigner-Moyal equation
* Phys.Rev.C79:034907,2009
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Introduction Quantum Semi-classical Comparison Conclusion
Roland Katz – 5/04/2013
The common tools
• “Weak potential F<V<U”
• “Strong potential V=U”
* Phys.Rev.D77:014501,2008 **arXiv:hep-lat/0512031v1
Evaluated by Mócsy & Petreczky* and Kaczmarek & Zantow** from some lQCD results and reparametrized by Gossiaux
The color potentials V(Tred, r)
F<V<UV=U
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The common tools
Introduction Quantum Semi-classical Comparison Conclusion
Roland Katz – 5/04/2013 * arXiv:nucl-th/0305084v2
• At fixed temperatures where
• Time dependent temperature Cooling of the QGP over time by
Kolb and Heinz* (hydrodynamic evolution and entropy conservation)
At LHC ( ) and RHIC ( ) energies
The temperature scenarios
Instantaneous transition from QGP at to hadronisation phase at .
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Introduction Quantum Semi-classical Comparison Conclusion
Quantum formalism
Roland Katz – 5/04/2013
• Schrödinger equation for the cc pair evolution
then expanded to the 1st degree in .
Where:
rc
c
QGP
reduced radial wave-function
with
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Introduction Quantum Semi-classical Comparison Conclusion
Quantum results
Roland Katz – 5/04/2013
With no color potential: V=0
• Projection onto the J/ψ state
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Introduction Quantum Semi-classical Comparison Conclusion
Roland Katz – 5/04/2013
Tred=0.4
With the weak color potential
(F<V<U) at fixed temperatures
Tred=0.6
Tred=0.8
Tred=1
Tred=1.4
With the weak color potential (F<V<U) and a
time-dependent temperature
RHICLHC
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Introduction Quantum Semi-classical Comparison Conclusion
Roland Katz – 5/04/2013
With the strong color potential (V=U) at fixed temperatures
Tred=0.4
Tred=0.8
Tred=1.2
Tred=1
Tred=1.4
Oscillations between 2 or 3 eigenstates for U(0.4<Tred <1.2)
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Introduction Quantum Semi-classical Comparison Conclusion
Roland Katz – 5/04/2013
With the strong color potential (V=U) and a time-dependent temperature
LHC
RHIC
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Introduction Quantum Semi-classical Comparison Conclusion
Semi-classical formalism
Roland Katz – 5/04/2013
The“Quantum” Wigner distribution of the cc pair:
… is evolved with the “classical”, 1st order in ħ, Wigner-Moyal equation:
Finally the projection onto the J/ψ state is given by:
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Introduction Quantum Semi-classical Comparison Conclusion
Roland Katz – 5/04/2013
But in practice: N test particles (initially distributed with the same gaussian distribution in (r, p) as in the quantum case), that evolve with Newton’s laws, and give the J/ψ weight at t with:
Semi-classical results
With no color potential: V=0
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Introduction Quantum Semi-classical Comparison Conclusion
Roland Katz – 5/04/2013
With the weak color potential
(F<V<U) at fixed temperatures
With the strong color potential (V=U) at fixed temperatures
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Introduction Quantum Semi-classical Comparison Conclusion
Roland Katz – 5/04/2013
From observing the distribution of test particles in the phase space over time:
The increase of Surv(J/ψ) for t < 0.5 fm/c <= some particles loose momentum while climbing the potential
And decrease of Surv(J/ψ) for t < 1 fm/c <= the particles with sufficient momentum go out the « J/ψ zone » by climbing the potential
Finally Surv(J/ψ) remains constant for t > 1 fm/c <= the latter particles reach the continuum
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Introduction Quantum Semi-classical Comparison Conclusion
Roland Katz – 5/04/2013
Relativistic 2 bodies dynamics instead of the previous non-relativistic relative one
Gives around 20 % lower J/ψ survival than the previous dynamics
Relativistic 2 bodies
dynamics
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Introduction Quantum Semi-classical Comparison Conclusion
Roland Katz – 5/04/2013
With additional stochastic and drag forces
The Langevin forces are added in Newton’s laws.
From observing the distribution of test particles in the phase space over time:
The increase of Surv(J/ψ) for t < … fm/c <= usual effect + an increased rate due to the drag force that keeps the particles to quit the “J/ψ zone”
And decrease of Surv(J/ψ) for t > … fm/c <= usual effects + with an increased rate, and during a longer time, effect due to the stochastic forces that continuously push the particles out of the “J/ψ zone”
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Introduction Quantum Semi-classical Comparison Conclusion
Roland Katz – 5/04/2013
ComparisonComparison of Surv[J/ψ](t->∞) average values function of Tred
Quantum approachSemi-classical approach
(no stochastic forces, relative dynamics)
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Introduction Quantum Semi-classical Comparison Conclusion
Roland Katz – 5/04/2013
Quantum Semi-classical
V=0 Same fast damping of the J/ψ state
Additionnal stochastic and
drag forcesFuture work
F<V<U
V=U Oscillations between 2 or 3 eigenstates for U(0.4<Tred <1.2)
The oscillations are damped No damping of the oscillations
Same remarks than for F<V<U
The mean values of Surv[J/ψ](t->∞) are quite different especially at large Tred
Has troubles to quit the interval around 1 of Surv[J/ψ]
Close result for both potentials
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Introduction Quantum Semi-classical Comparison Conclusion
Roland Katz – 5/04/2013
ConclusionThis project
The J/ψ survival in a screening medium -> studied with two different temperature dependent potentials and with two different approaches.
Strong discrepancies between the two approaches => the semi-classic approach proposed by Young and Shuryak may
not be relevant when quarkonia are studied in a color screened medium.
Future work The quantum approach should then be pursued -> • Bottomonia• Different additional stochastic and drag forces (<=> taking
into account the direct interactions with the medium particles)
Backup
With weak potential F<V<U with Tred from
0.4 to 1.4
With strong potential V=U
with Tred from 0.4 to 1.4
BackupAdditional stochastic forces